std:: sinh (std::complex)

Computes complex hyperbolic sine of a complex value z .

Parameters

Return value

If no errors occur, complex hyperbolic sine of z is returned.

Error handling and special values

Errors are reported consistent with math_errhandling .

If the implementation supports IEEE floating-point arithmetic,

• std:: sinh ( std:: conj ( z ) ) == std:: conj ( std:: sinh ( z ) )
• std:: sinh ( z ) == - std:: sinh ( - z )
• If z is (+0,+0) , the result is (+0,+0)
• If z is (+0,+∞) , the result is (±0,NaN) (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is (+0,NaN) , the result is (±0,NaN)
• If z is (x,+∞) (for any positive finite x), the result is (NaN,NaN) and FE_INVALID is raised
• If z is (x,NaN) (for any positive finite x), the result is (NaN,NaN) and FE_INVALID may be raised
• If z is (+∞,+0) , the result is (+∞,+0)
• If z is (+∞,y) (for any positive finite y), the result is +∞cis(y)
• If z is (+∞,+∞) , the result is (±∞,NaN) (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is (+∞,NaN) , the result is (±∞,NaN) (the sign of the real part is unspecified)
• If z is (NaN,+0) , the result is (NaN,+0)
• If z is (NaN,y) (for any finite nonzero y), the result is (NaN,NaN) and FE_INVALID may be raised
• If z is (NaN,NaN) , the result is (NaN,NaN)

where cis(y) is cos(y) + i sin(y) .

Notes

Hyperbolic sine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi .

Example

#include <cmath>
#include <complex>
#include <iostream>
 
int main()
{
    std::cout << std::fixed;
    std::complex<double> z(1.0, 0.0); // behaves like real sinh along the real line
    std::cout << "sinh" << z << " = " << std::sinh(z)
              << " (sinh(1) = " << std::sinh(1) << ")\n";
 
    std::complex<double> z2(0.0, 1.0); // behaves like sine along the imaginary line
    std::cout << "sinh" << z2 << " = " << std::sinh(z2)
              << " ( sin(1) = " << std::sin(1) << ")\n";
}

sinh(1.000000,0.000000) = (1.175201,0.000000) (sinh(1) = 1.175201)
sinh(0.000000,1.000000) = (0.000000,0.841471) ( sin(1) = 0.841471)

See also